1. Field of the Invention
The present invention relates to a control system for controlling the variable speed of an induction motor without an angular velocity detector.
2. Discussion of the Related Art
FIG. 14 is a circuit diagram showing a conventional control system for an induction motor, which is described in "The institute of Electric Engineers of Japan Trans., D", Vol. 112, No.9, p901, 1993 (referred to an article 1). In the figure, reference numeral 1 is excitation-current command computing means; 2 is as induction motor; 3 is torque control means; 4 is current detecting means; and 5 is parameter estimating means.
In the conventional induction-motor control system shown in FIG. 14, the excitation-current command computing means 1 receives a secondary magnetic flux .phi.dr* to be output by the induction motor 2, performs the operation of the following equation (20) in which an AC signal is added (superposed) to a DC signal proportional to the secondary magnetic flux .phi.dr*, and outputs an excitation-current command ids* of the induction motor 2.
[Formula 7] EQU ids*=(1+k1sing(2.pi.f1t)+k2sing(2.pi.f2t).phi.dr* M (20)
where
t: time PA1 k1: amplitude of a first superposing signal PA1 f1: frequency of the first superposing signal PA1 k2: amplitude of a second superposing signal PA1 f2: frequency of the second superposing signal PA1 current detecting means for detecting a primary current of an induction motor; PA1 excitation-current command computing means for receiving a secondary magnetic flux command to be output by the induction motor, and processing an AC signal and a DC signal proportional to the secondary magnetic flux command, to thereby produce an excitation current command of the induction motor; PA1 torque control means for receiving a torque command to be output by the induction motor and the excitation current command, and processing the estimated rotation angular velocity, the estimated secondary resistance and the primary current, and the torque control means controlling a primary voltage of the induction motor so that an output torque of the induction motor follows the torque command; PA1 first parameter estimating means for processing estimated primary resistance, the primary voltage and the primary current of the induction motor, to thereby produce the estimated rotation angular velocity and the estimated secondary resistance; and PA1 second parameter estimating means for processing the estimated rotation angular velocity, the estimated secondary resistance, the primary voltage and the primary current, to thereby produce the estimated primary resistance; PA1 wherein the first parameter estimating means includes PA1 the second parameter estimating unit includes PA1 current detecting means for detecting a primary current of an induction motor; PA1 excitation-current command computing means for receiving a secondary magnetic flux command to be output by the induction motor, and executing a process by use of the secondary magnetic flux command, to thereby produce an excitation current command of the induction motor; PA1 torque control means for receiving a torque command to be output by the induction motor and the excitation current command, and processing the estimated rotation angular velocity, the estimated secondary resistance and the primary current, and the torque control means controlling a primary voltage of the induction motor in accordance with the result of the processing so that an output torque of the induction motor follows the torque command; PA1 first parameter estimating means for processing estimated primary resistance, the estimated secondary resistance, the primary voltage and the primary current of the induction motor, to thereby produce the estimated rotation angular velocity; and PA1 second parameter estimating means for processing the estimated rotation angular velocity, the primary voltage and the primary current, to thereby produce the estimated primary resistance and the estimated secondary resistance; PA1 current detecting means for detecting a primary current of an induction motor; PA1 excitation-current command computing means for receiving a secondary magnetic flux command to be output by the induction motor, and processing an AC signal and a DC signal proportional to the secondary magnetic flux command, to thereby produce an excitation current command of the induction motor; PA1 torque control means for receiving a torque command to be output by the induction motor and the excitation current command, and processing the estimated rotation angular velocity, the estimated secondary resistance and the primary current, and the torque control means controlling a primary voltage of the induction motor so that an output torque of the induction motor follows the torque command; parameter estimating means for processing the primary voltage and the primary current of the induction motor, to thereby produce the estimated rotation angular velocity and the estimated secondary resistance; PA1 a) a measuring unit for processing estimated primary resistance, the estimated secondary resistance, the estimated rotation angular velocity, a feedback gain, the primary voltage and the primary current, to thereby produce estimated secondary current, estimated secondary magnetic flux and state deviation, PA1 b) a rotational-speed estimating unit for processing the state deviation and the estimated secondary magnetic flux, which are derived from the measuring unit, to thereby produce the estimated rotation angular velocity, PA1 c) a secondary-resistance estimating unit for processing the state deviation, the estimated secondary magnetic flux, and the estimated secondary current, which are derived from the measuring unit, to thereby produce the estimated secondary resistance, and PA1 d) a primary-resistance estimating unit for processing the estimated secondary resistance derived from the secondary-resistance estimating unit, to thereby produce the estimated primary resistance, PA1 e) a gain computing unit for processing the estimated rotation angular velocity derived from the rotational-speed estimating unit, to thereby produce the feedback gain so that the state deviation contains a component orthogonal to the estimated secondary magnetic flux, PA1 f) when a deviation is produced between the rotation angular velocity and the estimated rotation angular velocity of the induction motor, the gain computing unit produces a feedback gain causing a component orthogonal to the estimated secondary flux contained in the state deviation, and PA1 g) the secondary-resistance estimating unit executes a process by use of the product of a component being in phase with an estimated secondary magnetic flux contained the state deviation and another component being in phase with the estimated secondary magnetic flux contained in the estimated secondary current, to thereby produce an estimated secondary resistance. PA1 the measuring unit performs the operations of equations (14), (15) and (16), PA1 the gain computing unit performs the operation of an equation (17) defining the feedback gain, the rotational-speed estimating unit performs the operation of an equation (18) defining the estimated rotation angular velocity (18), and the secondary-resistance estimating unit performs the operation of an equation (19) defining the estimated secondary resistance
It is known that the excitation current must contain at least two frequency components in order to simultaneously estimate a rotation angular velocity and a secondary resistance of the induction motor.
The reason for this will be described. A circuit diagram shown in FIG. 15 is known as a T-type equivalent circuit where an excitation current is fixed in value. In the figure, cos is a slip angular velocity. To estimate a rotation angular velocity of the induction motor is equivalent to estimate a slip angular velocity in the figure since .omega.r=.omega.-.omega.s.
To simultaneously estimate a rotation angular velocity and a secondary resistance of the induction motor from the primary current and the primary voltage of the induction motor, which is controlled at a fixed excitation current, is equivalent to estimate Rr/.omega.s in the figure. Therefore, the principle makes it impossible to separate those one from the other.
Where the excitation current is not kept constant, .omega. and .omega.s are not fixed in value. The .omega. contains a plurality of components. The T-type equivalent circuit holds at each of the different slip angular velocities .omega.s for each of the components of the .omega.. Thus, the induction motor into which the control not keeping the excitation current constant is incorporated can simultaneously estimate the rotation angular velocity and the secondary resistance.
Accordingly, the superposing frequencies f1 and f2 sued are different in value, and in the conventional control system described in the article 1, those frequencies f1 and f2 are EQU f1=1 (Hz) EQU f2=3 (Hz)
In the article 1, the period of the first superposing signal is 1/f1, and the rating of the induction motor is 3.7 kw. In this sense, this signal is an AC signal having a period longer than a secondary time constant (=Lr/Rr) of the induction motor 2.
When a torque command .tau.m* to be output by the induction motor 2 and an excitation current command ids* from the excitation-current command computing means 1 are input to the torque control means 3, the torque control means 3 receives three-phase primary currents ius and ivs from the current detecting means 4, an estimated rotation angular velocity .omega. r0 from the current detecting means 4, and an estimated secondary resistance Rr0 from the parameter estimating means 5, and processes those factors so as that an output torque .tau.m of the induction motor follows .tau.m*, and supplies three-phase primary voltages vus, vvs, and vws to the induction motor.
The parameter estimating means 5 includes a measuring unit 6, a gain computing unit 7, a rotation velocity estimating unit 8, a secondary-resistance estimating unit 9, and a primary-resistance estimating unit 10.
The parameter estimating means 5 receives the primary voltage commands vus* and vvs* from the torque control means 3, and the primary currents ius and ivs from the current detecting means 4, and outputs an estimated rotation angular velocity .omega.r0 and an estimated secondary resistance Rr0.
The measuring unit 6 receives the primary current commands vus* and vvs* from the torque control means 3, the primary currents ius and ivs from the current detecting means 4, a feedback gain G from the gain computing unit 7, an estimated rotation angular velocity .omega.r0 from the rotation velocity estimating unit 8, and an estimated secondary resistance Rr0 from the secondary resistance estimating unit 9, and an estimated primary resistance Rs0 from the primary-resistance estimating unit 10, and performs the operations mathematical expressions (21), (22) and (23), to thereby produce an estimated primary current Is0, an estimated secondary current Ir0, a state deviation E, and an estimated secondary magnetic flux .phi.r0.
[Formula 8] ##EQU1##
The gain computing unit 7 produces a feedback gain G, which is given by the equation (24) containing the estimated rotation angular velocity .omega.r0, which is received from the rotational speed estimating unit 8. ##EQU2##
The number of poles of the measuring unit 6 is k times as large as that of the induction motor 2 when the feedback gain G given by the equation (24) is used.
The rotational speed estimating unit 8 receives the estimated secondary magnetic flux .phi.r0 and the state deviation E from the measuring unit 6, and computes an outer product E.times..phi.r0, and corrects the estimated rotation angular velocity .omega.r0, which is used in the measuring unit, by use of an equation (25), and outputs the corrected one.
[Formula 10] ##EQU3##
The secondary-resistance estimating unit 9 receives the estimated secondary current ir0 and the state deviation E from the measuring unit 6, and computes an inner product E.multidot.ir0, and corrects the estimated secondary resistance Rr0 used in the measuring unit 6 by use of the equation (26), and outputs the corrected one.
[Formula 11] ##EQU4##
The primary-resistance estimating unit 10 receives the estimated primary current is0 and the state deviation E from the measuring unit 6, and computes an inner product E.multidot.is0, and corrects the estimated primary resistance Rs0 by use of an equation (27) used in the measuring unit 6, and outputs the corrected one.
[Formula 12] ##EQU5##
The parameter estimating means 5, which is thus constructed and operated, outputs an estimated rotation angular velocity .omega.r0 and an estimated secondary resistance Rr0.
FIG. 17 is a diagram showing the detail of the torque control means 3. In the figure, reference numeral 11 is a torque-current command computing unit; 12 is a primary-angular-velocity computing unit; 13 is an integrator; 14 is a coordinate transformer for transforming a primary current on the static coordinates to that on the rotation coordinates; 15 and 16 are subtractors; 17 and 18 are current controllers; 19 is a coordinate transformer for transforming a primary voltage command on the rotational coordinates into that on the static coordinates; and 20 is a PWM inverter.
The following mathematical expression (28) holds among a generated torque .tau.m, an amplitude .phi.dr of a secondary magnetic flux, and a torque current iqs.
[Formula 13] EQU iqs{character pullout}.tau.m/.phi.dr (28)
Therefore, the torque-current command computing unit 11 divides an input torque command .tau.m* by a secondary-magnetic-flux amplitude computed value .phi.dr1 received from the primary-angular-velocity computing unit 12, multiplies the resultant by a constant number; and outputs the resultant as a torque current command iqs*.
The primary-angular-velocity computing unit 12 receives the input excitation-current command ids*, a torque current command iqs*, an estimated secondary resistance Rr0, and an estimated rotation angular velocity .omega.r0, and computes a secondary-magnetic- flux amplitude computed value .phi.dr1 and a primary angular velocity .omega. by use of the following equations (29) and (30).
[Formula 14] ##EQU6##
The integrator 13 integrates a primary angular velocity .omega., which is received from the primary-angular-velocity computing unit 12, and outputs a phase angle .theta..
The coordinate transformer 14 coordinate-transforms the primary currents ius and ivs, which are derived from the current detecting means 4, into those on the rotation 2-axes coordinates in accordance with the phase angle .theta..
The subtractor 15 subtracts the excitation current ids from the excitation current command iqs* to produce a difference signal. The subtractor 16 subtracts the torque current iqs* from the torque current command iqs* to produce a difference signal.
The current controller 17 amplifies the difference signal, which is derived from the subtractor 15, so that the excitation current ids follows the excitation current command ids*, and outputs the resultant in the form of a d-axis voltage command vds*.
The current controller 18 amplifies the difference signal, which is derived from the subtractor 16, so that the torque current iqs follows the torque current command iqs* and outputs the resultant in the form of q-axis voltage command vqs*.
The coordinate transformer 19 coordinate-transforms d- and q-axis voltage commands vds* and vqs*, which are derived from the current controllers 17 and 18, into those on the 3-phase static coordinates in accordance with the phase angle .theta., and produces 3-phase voltage commands vus*, vvs* and vws*.
The PWM inverter 20 receives the 3-phase voltage commands vus*, vvs* and vws*, and supplies 3-phase primary voltages vus, uvs, and vws to the induction motor 2.
In the thus constructed control system for the induction motor, even when the induction motor 2 is heated and its temperature varies, and the primary and secondary resistance values vary, the estimated primary and secondary resistance follow the primary and secondary variations. Therefore, the control system can control the induction motor without the rotation angular velocity sensor so that the output torque .tau.m of the induction motor 2 follows the torque command rm*.
However, the conventional induction-motor control system has the following problems: 1) Estimation of the primary resistance is impossible in the regenerative region. 2) An accuracy of an estimated secondary resistance depends largely on the primary frequency. 3) Torque ripples occur in the output torque .tau.m. 4) A number of operations are required in preparing a plurality of frequencies of AC components of the excitation current. 5) It is relatively difficult to separately estimate the secondary resistance and the rotation angular velocity.
The first problem 1) above will be described. A vector diagram describing a relationship among the state deviation E, the primary current is, and the estimated primary current is0 is shown in FIG. 16. Discussion will be given by use of the vector diagram.
The primary current is is not coincident in vector with the estimated primary current is0 when a deviation is present between the rotation angular velocity .omega.r and the estimated rotation angular velocity .omega.r0, a deviation is present between the secondary resistance Rr and the estimated secondary resistance Rr0, and a deviation is present between the primary current rs and the estimated primary current is.
Where a deviation is present between the estimated value and the true value, a relationship among the primary current is, the estimated primary current is0, and the state deviation is mathematically expressed as E=(is0-is) and those vectors are depicted as shown in FIG. 16.
The coordinates in FIG. 16 are the d-q axes plane (static coordinates) which rotate at a frequency .omega. in synchronism with the estimated secondary magnetic flux .phi.r0.
The primary resistance estimating unit 10 estimates an estimated primary resistance by performing the operation of the equation (27). The integrated term (is0.multidot.E) in the equation is the inner product of the estimated primary current is0 and the state deviation (primary current error) (E).
Where the amplitude .vertline.is0.vertline. of the estimated primary current is constant, the integrated term takes a value proportional to a component being in phase with the estimated primary current is0 of the state deviation E.
FIG. 18A is a vector diagram showing a relationship between the estimated primary current is0 and the state deviation E when a difference (error) is present between the primary resistance Rs and the estimated primary resistance Rs0 of the induction motor.
It is assumed that when a phase difference between is0 and E, E=.xi..alpha., E is E.alpha., and that when a phase difference .xi. between is0 and E is .xi..beta., E=E.beta..
When the phase difference is .xi..alpha., the value of the integrated term E.multidot.is0 (=.vertline.E.vertline..vertline.is0.vertline.cos .xi.) is smaller than that when the phase difference .xi. is 0.degree.. Therefore, the operation of the equation (27) is sensitive to noise, and improvement of its estimating response is impossible.
When the phase difference is .xi..beta., a sign of the integrated term (E.multidot.is0) is inverted. If the equation (27) is operated under this condition, the equation of the estimated primary resistance forms a positive feedback loop, and diverges.
In summary, when .vertline..xi..vertline.90.degree., the estimating operation (performing of the operation of the equation (27)) is stable, and the integrated term (E.multidot.is0) becomes small as .vertline..xi..vertline. approaches to 90.degree.. When .vertline..xi..vertline.=90.degree., the (E.multidot.is0) is 0 in value and hence the estimating operation is impossible. When .vertline..xi..vertline.&lt;90.degree., the estimating operation is unstable.
Consequently, it is desirable that the state deviation E is in phase with the estimated primary current is0 (phase difference .xi.=0.degree.). In this condition, the estimating operation of the primary resistance is stable and highly accurate.
FIG. 19A is a graph showing an exemplary relationship between the phase difference .xi. and the primary angular velocity .omega., which is derived from the conventional parameter estimating means 5 (rotation angular velocity .omega.r is 100 (rad/s)). In the figure, the abscissa represents an angular velocity (i.e., the primary angular velocity .omega.) of the estimated primary current is0, and the ordinate represents an phase difference .xi. between the estimated primary current is0 and the status deviation E.
In FIG. 19A, "k" represents a parameter of the gain computing unit 7. As seen, the .xi.-.omega. characteristic varies with the parameter "k". Where "k" is large, .vertline..xi..vertline.&gt;90.degree. and the equation (27) of the estimated primary resistance Rs0 diverges.
Further, a frequency region where .omega.r0&lt;100 (rad/s) contains a region where .vertline..xi..vertline.&gt;90.degree.. This fact implies that the estimating operation of the estimated primary resistance diverges in a region where the primary angular velocity is lower than the rotation angular velocity, viz., in the regenerative region.
As seen from FIG. 19A, in the conventional induction motor control system, the phase difference .xi. does not take a desired value (0.degree., constant) for in the specific region of the primary angular velocity .omega.. Therefore, the estimating operation of the estimated primary resistance is instable, for example, its response is poor or it diverges. This leads to degradation of the accuracy and the response of operating the rotation angular velocity .omega.r0 and the estimated secondary resistance Rr0, and diverging in their operations.
In this state, the rotation angular velocity .omega.r0 and the estimated secondary resistance Rr0, which contain errors, are input to the torque control means 3. The output torque .tau.m fails to follow the torque command .tau.m* or another instable phenomenon occurs.
The second problem of 2) above will be described.
The secondary-resistance estimating unit 9 operates the equation (26) for producing an estimated secondary resistance. In the equation, the integrated term (ir0.multidot.E) is the inner product of the estimated secondary current ir0 and the state deviation (primary current error) E.
If the amplitude .vertline.ir0.vertline. of the estimated secondary current is fixed in value, the integrated term (ir0.multidot.E) takes a value proportional to a component being in phase with the estimated secondary current ir0 of the state deviation E.
FIG. 18B is a vector diagram showing a relationship between the estimated secondary current ir0 and the state deviation E when a difference (error) is present between the secondary resistance Rr and the estimated secondary resistance Rr0.
It is assumed that E=E.rho. when the phase difference .xi. between the estimated secondary current ir0 and the state deviation E is phase difference .xi..rho., and that E is E.sigma. when the phase difference .xi. between the estimated secondary current ir0 and the state deviation is .xi..sigma..
When the phase difference=.xi..sigma., the integrated term (ir0.multidot.E) (=.vertline.E.vertline..vertline.ir0.vertline.cos .xi.) is smaller in value than when the .xi.=0.degree.. In this case, the operation of the equation (26) is sensitive to noise, and its response improvement is impossible.
When the phase difference=.xi..sigma., the sign of the value of the integrated term (ir0.multidot.E) is inverted. In this state, the equation (26) of the estimated secondary resistance forms a positive feedback loop, and diverges.
In summary, when .vertline..xi..vertline.&lt;90.degree., the secondary-resistance estimating operation is stable, but as .vertline..xi..vertline. approaches to 90.degree., the integrated term (ir0.multidot.E) becomes small. When .vertline..xi..vertline.=90.degree., (ir0.multidot.E)=0 and the estimating operation is impossible. When .vertline..xi..vertline.&gt;90.degree., the estimating operation is unstable.
As seen, it is desirable that the state deviation E is in phase with the estimated secondary current ir0 (phase difference .xi.=0.degree.). Where this condition is satisfied, the estimating operation of the secondary resistance estimation is stable and highly accurate.
FIG. 20A is a graph showing an exemplary relationship between the phase difference .xi. and the primary angular velocity .omega., which are derived from the conventional parameter estimating means 5 (rotation angular velocity .omega.r=100 (rad/s). In the graph, the abscissa represents the angular velocity of the ir0 (i.e., primary angular velocity .omega.), and the ordinates represents a phase difference .xi. between the ir0 and the E.
In FIG. 20A, "k" represents a parameter "k" in the gain computing unit 7. As seen, a profile of the .xi.-.omega. characteristic varies depending on the value of the parameter "k". When "k" is small, .vertline..xi..vertline.&gt;90.degree. and the equation of the estimated secondary resistance Rr0 diverges.
In high frequencies, .xi.=-90.degree. irrespective of the value of "k". This state means that (ir0.multidot.E)=0, and that the estimating operation of the secondary resistance is impossible.
As seen from FIG. 20A, in the conventional control system for the induction motor, the phase difference .xi. cannot take a desired value. Therefore, the operation for estimating the secondary resistance is slow in its response or diverges (viz., it is unstable). The result is that the accuracy and response of the estimated rotation angular velocity .omega.r0 and the estimated primary resistance Rs0 are deteriorated or sometimes the operated value diverges.
In this state, the estimated rotation angular velocity .omega.r0 and the estimated secondary resistance Rr0, which contain errors, are input to the torque control means 3. As a result, the output torque .tau.m fails to follow the torque command .tau.m* or the estimating operation is unstable.
The third problem 3) above will then be described. FIG. 21 is a graph showing a transfer characteristic from the excitation current ids to (.o slashed. dr/M) and idr. The first and second frequency coefficients of the conventional control system in which an AC signal is given by the equation (20) contain frequency components sufficiently shorter in periods than the reciprocal (number) of the secondary time constant, 1/Tr.
When the secondary magnetic-flux amplitude .phi.dr of the induction motor 2 varies, the value of the mutual inductance M varies due to magnetic saturation. Therefore, the secondary magnetic-flux amplitude .PHI.dr being fixed in value is desirable to secure a desired torque in the control of the induction motor.
As seen from the FIG. 21, when the excitation current ids contains frequency components shorter in period than 1/Tr, the secondary magnetic-flux amplitude .o slashed.dr also contains those frequency components. Therefore, the mutual inductance M also contains those frequency components. The AC components appear as torque ripples in the output torque .tau.m, and hence it is not coincident with the torque command .tau.m*.
The fourth problem 4) above will now be described.
In the conventional induction-motor control system, to prepare "n" kinds of AC components of the excitation current, it is necessary to perform, "n" times, the operations of "k1 sin(2.pi.f1t)+k2 sin(2.pi.f2t)+k3sin(2.pi.f3t)+. . . kn sin (2.pi.fnt) and the operations of the sine function. The operation of the sine function is more complicated than the operations of addition, subtraction, and multiplication, and hence consumes much time.
Finally, the fifth problem 5) above will be described.
The conventional induction-motor control system estimates a rotation angular velocity by use of the quadrature component of the estimated secondary magnetic flux of the state deviation E {(J.o slashed.r0).sup.T E} (equation (25)). Further, it estimates a secondary resistance by use of the component (E.multidot.ir0) of the state deviation E being in phase with the estimated secondary current ir0 (equation (26)).
Where the frequencies of the AC components of the excitation current ids are low or their amplitudes are small, the d-axis component idr of the secondary current is small. Where the d-axis component idr is small, the qu-axis component is dominant. In this case, the secondary current is substantially equal to the component (q-axis component) orthogonal to the estimated secondary magnetic flux. Therefore, the quadrature component {(J.o slashed. r0).sup.T E} is substantially equal in value to the in-phase component (E.multidot.ir0). Thus, the function of the quadrature component of the estimated secondary magnetic flux is used for both the rotational speed estimation and the secondary resistance estimation. Therefore, it is impossible to estimate the secondary resistance and the rotation angular velocity separately.